LEI - Writing Equations of Lines (Lesson)

Writing Equations of Lines

Now that you know how to graph lines, we want to learn how to write the equations of lines. First, you need to know one more formula:

Point-Slope: y - y₁= m(x - x₁)

Example: Write the equation in slope-intercept form of the line with slope 2 that contains the point (5, -3).

Step 1: Substitute a point in for x₁ and y₁ and use the slope for m. Simplify as needed.

y - (-3) = 2 (x - 5)
y + 3 = 2 (x - 5)

Step 2: To change to slope-intercept form, isolate y.

y + 3 = 2x - 10
y = 2x - 13

Watch this video for some more practice.

Make sure you have this!!! Do you see how we got the equations below??

Contains the points (2, 4) and (-2, 2) / y = (1/2)x + 3
Contains the point (3, -2) and has a slope of 0 / y = -2
Contains the points (3, -2) and (3, 7) / x = 3
Contains the point (2, -5) and has a slope of -3 / y = -3x + 1
Contains the points (1, -8) and (9, 0) / y = x - 9
Contains the point (-4, 1) and has an undefined slope / x = -4

Now let us imagine that you are riding in a taxi-cab. The cab charges an initial fee once you get in and then a charge per mile driven. You notice that after you have gone 3 miles, the charge is $8 and after 9 miles the charge is $17. Write a function, C, to represent the cost of the taxicab after driving a certain number of miles, x.

The first step for this problem is determining which of the given information represents the independent and dependent variables:

Independent Variable: miles driven in taxi; x = 3; x = 9

Dependent Variable: cost of taxi; C(3) = 8; C(9) = 17

So now let us find the rate of change, or the slope for the function:

Rate of change: (17 - 8)/(9 - 3) = 9/6 = 1.5

And now lets use the point-slope formula to write an equation:

y - 8 = 1.5(x - 3)

y - 8 = 1.5x - 4.5

y = 1.5x + 3.5

Use the equation we found to answer the following questions:

What is the initial cost for the taxi before driving any miles?
What is the cost per mile for the taxi?
How much will the fare be if you drive 12 miles?
If you paid $14, how many miles did you drive?
What is the domain, or input for this situation?

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

Watch this video to practice more problems like this one:

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